Effective Medium Perspective on Topological Transitions in Metamaterials

TL;DR

This paper explores how effective medium theory can describe topological phase transitions in subwavelength metamaterials, linking changes in permittivity and permeability to topological invariants in structures with $D_6$ symmetry.

Contribution

It introduces an effective medium perspective to analyze topological transitions in deeply subwavelength metamaterials, connecting material parameters to topological properties.

Findings

Permittivity and permeability change during topological transitions.

Effective medium theory describes topological phases in subwavelength structures.

Analysis focused on structures with $D_6$ symmetry.

Abstract

Many properties of photonic structures rely on band topology characterized by the integer invariants that can change during the topological transitions and give rise to the disorder-robust topological edge, corner, or interface states. Typically the periods of such structures are comparable to the wavelength. However, in many cases, the unit cell becomes deeply subwavelength and hence the entire metamaterial can be described in terms of the effective material parameters. Here, focusing on subwavelength topological metamaterials, we identify the behavior of permittivity and permeability accompanying the topological transition on the example of the two structures possessing $D_6$ symmetry.